A symmetry-extension construction of an anomalous 4d Z_{N_c}-gauge TQFT cancels the SM mixed anomaly and selects N_c = N_f = 3 as the unique odd-color solution.
Anomalies of 4d Spin G theories
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Superconductors are bosonic at low energy yet carry a gravito-magnetic anomaly from fermion parity gauging that forbids trivial massive phases in 3D and 4D.